2, there are practical situations where duality does not provide satisfactory answer to strong type (p,p) issues. In collaboration with Coulhon, Duong and Hofmann I obtained a criterion (sufficient condition) for testing directly strong type (p,p) for a given p in (2,\infty). This criterion is based upon recent of Martell, who introduced a sharp function that replaces that of Fefferman-Stein. I will explain the two criteria and give applications towards results on Riesz transforms (for elliptic operators on the euclidean space or the Laplace-Beltrami operator on a manifold), square functions and functional calculi I will show in particular that the ranges of p's are not necessarily (1,\infty) and also that these criteria give optimal ranges of p's. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%